The source of the data is here: https://archive.ics.uci.edu/ml/datasets/Wine+Quality
Original citation: P. Cortez, A. Cerdeira, F. Almeida, T. Matos and J. Reis. Modeling wine preferences by data mining from physicochemical properties. In Decision Support Systems, Elsevier, 47(4):547-553, 2009.
This data consists of two datasets. Each dataset contains quality ratings for wines as well as 11 features of these wines. The 12 variables are all continuous and numeric. The first dataset contains 1599 observations of red wines; the second dataset contains 4898 observations of white wines.
df <- as_tibble(read.table("winequality-red.csv", sep=";", header = TRUE))
summary(df$quality)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.636 6.000 8.000
df_white <- as_tibble(read.table("winequality-white.csv", sep=";", header = TRUE))
summary(df_white$quality)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.878 6.000 9.000
The variables in the data all have different scales. For example:
summary(df$fixed.acidity)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.60 7.10 7.90 8.32 9.20 15.90
summary(df$sulphates)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3300 0.5500 0.6200 0.6581 0.7300 2.0000
The data will be standardized to make some plots of the data easier to visualize.
data_red <- as.data.frame(scale(df))
summary(data_red$fixed.acidity)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.1364 -0.7005 -0.2410 0.0000 0.5056 4.3538
data_white <- as.data.frame(scale(df_white))
summary(data_white$sulphates)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.3645 -0.6996 -0.1739 0.0000 0.5271 5.1711
Glancing at the raw data, we see that the red wine quality ratings are not distributed uniformly, and there are a few outlier ratings. Our model will probably not perform well when predicting red wine ratings below 4 or above 7.
hist(df$quality,
main="Histogram of Red Wine Quality Ratings",
xlab="Rating",
las=1,
breaks=4)
The white wine ratings are distributed similarly, although a bit more symmetrically. Our model will probably not perform well when predicting white wine ratings below 4 or above 8.
hist(df_white$quality,
main="Histogram of White Wine Quality Ratings",
xlab="Rating",
las=1,
breaks=5)
We may consider winsorizing or truncating our dataset to only consider observations where the rating was above 4 and below 7 (or 8, for white wine).
Looking at the standardized data, there are a few variables that immediately appear to be predictive of the quality. Alcohol is one:
ggplot(data_red, aes(x=alcohol, y=quality)) +
geom_point() +
geom_smooth(method=lm) +
labs(title="Alcohol Content vs. Quality Rating",
subtitle="Red Wine",
y="Quality",
x="Alcohol")
Volatile acidity is another one:
ggplot(data_red, aes(x=volatile.acidity, y=quality)) +
geom_point() +
geom_smooth(method=lm) +
labs(title="Volatile Acidity vs. Quality Rating",
subtitle="Red Wine",
y="Quality",
x="Acidity")
These variables will likely be useful for predicting quality ratings of white wine as well:
ggplot(data_white, aes(x=alcohol, y=quality)) +
geom_point() +
geom_smooth(method=lm) +
labs(title="Alcohol Content vs. Quality Rating",
subtitle="White Wine",
y="Quality",
x="Alcohol")
ggplot(data_white, aes(x=volatile.acidity, y=quality)) +
geom_point() +
geom_smooth(method=lm) +
labs(title="Volatile Acidity vs. Quality Rating",
subtitle="White Wine",
y="Quality",
x="Acidity")
The data will be split into train and test datasets. The model will be trained on the train data and evaluated on the test data.
index = sample(1:nrow(df), 0.7*nrow(df))
train = df[index,] # Create the training data
test = df[-index,] # Create the test data
dim(train)
## [1] 1119 12
dim(test)
## [1] 480 12
lm_basic <- lm(data = df, quality ~ .)
summary(lm_basic)
##
## Call:
## lm(formula = quality ~ ., data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.68911 -0.36652 -0.04699 0.45202 2.02498
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.197e+01 2.119e+01 1.036 0.3002
## fixed.acidity 2.499e-02 2.595e-02 0.963 0.3357
## volatile.acidity -1.084e+00 1.211e-01 -8.948 < 2e-16 ***
## citric.acid -1.826e-01 1.472e-01 -1.240 0.2150
## residual.sugar 1.633e-02 1.500e-02 1.089 0.2765
## chlorides -1.874e+00 4.193e-01 -4.470 8.37e-06 ***
## free.sulfur.dioxide 4.361e-03 2.171e-03 2.009 0.0447 *
## total.sulfur.dioxide -3.265e-03 7.287e-04 -4.480 8.00e-06 ***
## density -1.788e+01 2.163e+01 -0.827 0.4086
## pH -4.137e-01 1.916e-01 -2.159 0.0310 *
## sulphates 9.163e-01 1.143e-01 8.014 2.13e-15 ***
## alcohol 2.762e-01 2.648e-02 10.429 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1587 degrees of freedom
## Multiple R-squared: 0.3606, Adjusted R-squared: 0.3561
## F-statistic: 81.35 on 11 and 1587 DF, p-value: < 2.2e-16
Volatile acidity, chlorides, total sulfur dioxide, sulphates and alcohol are all very statistically significant, although our adjusted \(R^2\) is still quite low.
train_control <- trainControl(method = "cv", number = 5)
model_ridge <- train(quality ~ .,
data = df,
method = "ridge", # method
trControl = train_control) # cross validation
model_ridge
## Ridge Regression
##
## 1599 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 1279, 1280, 1280, 1279, 1278
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0e+00 0.6508382 0.3530946 0.5040202
## 1e-04 0.6508355 0.3531007 0.5040170
## 1e-01 0.6504340 0.3546738 0.5027356
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 0.1.
#something doesn't seem to be working here
model_stepwise <- train(quality ~ .,
data = df,
method = "glmStepAIC",
trControl = train_control)
## Start: AIC=2474.52
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 507.95 2472.6
## - density 1 508.01 2472.7
## - fixed.acidity 1 508.12 2473.0
## - citric.acid 1 508.37 2473.6
## <none> 507.94 2474.5
## - pH 1 508.93 2475.0
## - free.sulfur.dioxide 1 509.72 2477.0
## - chlorides 1 514.60 2489.2
## - total.sulfur.dioxide 1 516.99 2495.1
## - volatile.acidity 1 532.67 2533.3
## - sulphates 1 535.93 2541.1
## - alcohol 1 543.89 2560.0
##
## Step: AIC=2472.56
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + density + pH +
## sulphates + alcohol
##
## Df Deviance AIC
## - density 1 508.01 2470.7
## - fixed.acidity 1 508.13 2471.0
## - citric.acid 1 508.38 2471.6
## <none> 507.95 2472.6
## - pH 1 509.14 2473.6
## - free.sulfur.dioxide 1 509.81 2475.2
## - chlorides 1 514.62 2487.2
## - total.sulfur.dioxide 1 517.02 2493.2
## - volatile.acidity 1 532.76 2531.5
## - sulphates 1 536.68 2540.9
## - alcohol 1 556.16 2586.5
##
## Step: AIC=2470.71
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 508.13 2469.0
## - citric.acid 1 508.45 2469.8
## <none> 508.01 2470.7
## - free.sulfur.dioxide 1 509.88 2473.4
## - pH 1 509.93 2473.5
## - chlorides 1 514.86 2485.8
## - total.sulfur.dioxide 1 517.45 2492.2
## - volatile.acidity 1 533.56 2531.5
## - sulphates 1 537.01 2539.7
## - alcohol 1 593.10 2666.8
##
## Step: AIC=2469.01
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 508.45 2467.8
## <none> 508.13 2469.0
## - free.sulfur.dioxide 1 510.08 2471.9
## - pH 1 511.61 2475.7
## - chlorides 1 515.85 2486.3
## - total.sulfur.dioxide 1 518.84 2493.7
## - volatile.acidity 1 534.32 2531.3
## - sulphates 1 537.60 2539.1
## - alcohol 1 593.56 2665.8
##
## Step: AIC=2467.82
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 508.45 2467.8
## - free.sulfur.dioxide 1 510.68 2471.4
## - pH 1 511.72 2474.0
## - chlorides 1 516.82 2486.7
## - total.sulfur.dioxide 1 520.04 2494.7
## - sulphates 1 537.62 2537.2
## - volatile.acidity 1 539.17 2540.8
## - alcohol 1 594.93 2666.7
## Start: AIC=2547.9
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 538.63 2546.6
## - residual.sugar 1 538.94 2547.3
## - citric.acid 1 539.01 2547.5
## - fixed.acidity 1 539.04 2547.6
## <none> 538.34 2547.9
## - pH 1 539.27 2548.1
## - free.sulfur.dioxide 1 539.63 2549.0
## - chlorides 1 545.45 2562.7
## - total.sulfur.dioxide 1 545.79 2563.5
## - sulphates 1 557.36 2590.3
## - volatile.acidity 1 561.73 2600.2
## - alcohol 1 574.16 2628.2
##
## Step: AIC=2546.58
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 538.95 2545.3
## - fixed.acidity 1 539.08 2545.7
## - citric.acid 1 539.31 2546.2
## <none> 538.63 2546.6
## - free.sulfur.dioxide 1 540.02 2547.9
## - pH 1 540.97 2550.1
## - chlorides 1 546.07 2562.1
## - total.sulfur.dioxide 1 546.29 2562.6
## - sulphates 1 557.67 2589.0
## - volatile.acidity 1 563.09 2601.3
## - alcohol 1 638.45 2761.9
##
## Step: AIC=2545.34
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 539.47 2544.6
## - citric.acid 1 539.57 2544.8
## <none> 538.95 2545.3
## - free.sulfur.dioxide 1 540.50 2547.0
## - pH 1 541.25 2548.8
## - chlorides 1 546.20 2560.4
## - total.sulfur.dioxide 1 546.39 2560.9
## - sulphates 1 557.75 2587.2
## - volatile.acidity 1 563.14 2599.5
## - alcohol 1 640.92 2764.8
##
## Step: AIC=2544.58
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 539.69 2543.1
## <none> 539.47 2544.6
## - free.sulfur.dioxide 1 541.22 2546.7
## - pH 1 544.60 2554.7
## - chlorides 1 548.29 2563.3
## - total.sulfur.dioxide 1 548.95 2564.8
## - sulphates 1 558.85 2587.7
## - volatile.acidity 1 563.39 2598.0
## - alcohol 1 641.46 2763.9
##
## Step: AIC=2543.1
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 539.69 2543.1
## - free.sulfur.dioxide 1 541.65 2545.7
## - pH 1 545.13 2553.9
## - chlorides 1 549.03 2563.0
## - total.sulfur.dioxide 1 549.91 2565.1
## - sulphates 1 558.87 2585.7
## - volatile.acidity 1 568.21 2606.9
## - alcohol 1 643.75 2766.4
## Start: AIC=2532.13
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - free.sulfur.dioxide 1 531.19 2530.7
## - fixed.acidity 1 531.37 2531.2
## - density 1 531.49 2531.4
## <none> 530.94 2532.1
## - citric.acid 1 531.80 2532.2
## - pH 1 532.10 2532.9
## - residual.sugar 1 532.66 2534.3
## - total.sulfur.dioxide 1 535.66 2541.5
## - chlorides 1 537.41 2545.6
## - sulphates 1 552.84 2581.9
## - volatile.acidity 1 562.91 2605.0
## - alcohol 1 563.50 2606.3
##
## Step: AIC=2530.73
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + total.sulfur.dioxide + density + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 531.69 2529.9
## - density 1 531.81 2530.2
## <none> 531.19 2530.7
## - pH 1 532.22 2531.2
## - citric.acid 1 532.23 2531.2
## - residual.sugar 1 533.16 2533.5
## - total.sulfur.dioxide 1 537.22 2543.2
## - chlorides 1 537.53 2543.9
## - sulphates 1 553.39 2581.2
## - alcohol 1 563.58 2604.5
## - volatile.acidity 1 565.08 2607.9
##
## Step: AIC=2529.94
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + total.sulfur.dioxide + density + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - density 1 531.83 2528.3
## - citric.acid 1 532.40 2529.6
## <none> 531.69 2529.9
## - residual.sugar 1 533.18 2531.5
## - pH 1 536.56 2539.6
## - total.sulfur.dioxide 1 538.75 2544.8
## - chlorides 1 539.26 2546.0
## - sulphates 1 553.40 2579.2
## - volatile.acidity 1 565.36 2606.5
## - alcohol 1 586.54 2653.6
##
## Step: AIC=2528.27
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 531.83 2528.3
## - citric.acid 1 533.12 2529.4
## - residual.sugar 1 533.24 2529.7
## - pH 1 536.72 2538.0
## - total.sulfur.dioxide 1 538.81 2542.9
## - chlorides 1 539.26 2544.0
## - sulphates 1 553.68 2577.8
## - volatile.acidity 1 569.31 2613.4
## - alcohol 1 628.85 2740.8
## Start: AIC=2552.28
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 539.37 2550.3
## - fixed.acidity 1 539.39 2550.3
## - density 1 539.41 2550.4
## - citric.acid 1 539.63 2550.9
## <none> 539.37 2552.3
## - free.sulfur.dioxide 1 541.75 2555.9
## - pH 1 543.22 2559.4
## - total.sulfur.dioxide 1 546.04 2566.0
## - chlorides 1 547.69 2569.9
## - sulphates 1 560.91 2600.4
## - volatile.acidity 1 568.67 2618.0
## - alcohol 1 577.06 2636.7
##
## Step: AIC=2550.29
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + density + pH +
## sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 539.39 2548.3
## - density 1 539.41 2548.4
## - citric.acid 1 539.63 2548.9
## <none> 539.37 2550.3
## - free.sulfur.dioxide 1 541.81 2554.1
## - pH 1 543.83 2558.8
## - total.sulfur.dioxide 1 546.04 2564.0
## - chlorides 1 547.72 2567.9
## - sulphates 1 561.75 2600.3
## - volatile.acidity 1 568.69 2616.1
## - alcohol 1 590.12 2663.4
##
## Step: AIC=2548.33
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 539.41 2546.4
## - citric.acid 1 539.64 2546.9
## <none> 539.39 2548.3
## - free.sulfur.dioxide 1 541.87 2552.2
## - total.sulfur.dioxide 1 546.80 2563.8
## - pH 1 548.11 2566.9
## - chlorides 1 548.50 2567.8
## - sulphates 1 561.81 2598.5
## - volatile.acidity 1 568.75 2614.2
## - alcohol 1 601.67 2686.2
##
## Step: AIC=2546.39
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 539.85 2545.4
## <none> 539.41 2546.4
## - free.sulfur.dioxide 1 541.88 2550.2
## - total.sulfur.dioxide 1 546.81 2561.8
## - pH 1 548.18 2565.0
## - chlorides 1 548.59 2566.0
## - sulphates 1 562.37 2597.7
## - volatile.acidity 1 572.50 2620.6
## - alcohol 1 635.71 2754.6
##
## Step: AIC=2545.43
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 539.85 2545.4
## - free.sulfur.dioxide 1 542.63 2550.0
## - total.sulfur.dioxide 1 547.87 2562.3
## - pH 1 548.84 2564.6
## - chlorides 1 549.97 2567.2
## - sulphates 1 562.43 2595.9
## - volatile.acidity 1 579.40 2633.9
## - alcohol 1 637.20 2755.6
## Start: AIC=2558.93
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 542.99 2557.9
## - fixed.acidity 1 543.07 2558.1
## - citric.acid 1 543.08 2558.1
## - residual.sugar 1 543.42 2558.9
## <none> 542.59 2558.9
## - pH 1 544.11 2560.5
## - free.sulfur.dioxide 1 544.39 2561.2
## - chlorides 1 547.76 2569.1
## - total.sulfur.dioxide 1 549.16 2572.3
## - sulphates 1 560.96 2599.5
## - volatile.acidity 1 567.47 2614.3
## - alcohol 1 582.23 2647.1
##
## Step: AIC=2557.86
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 543.09 2556.1
## - residual.sugar 1 543.43 2556.9
## - citric.acid 1 543.48 2557.0
## <none> 542.99 2557.9
## - free.sulfur.dioxide 1 544.93 2560.4
## - pH 1 546.84 2564.9
## - chlorides 1 548.55 2568.9
## - total.sulfur.dioxide 1 549.81 2571.8
## - sulphates 1 561.19 2598.0
## - volatile.acidity 1 569.06 2615.8
## - alcohol 1 645.62 2777.3
##
## Step: AIC=2556.1
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 543.49 2555.0
## - residual.sugar 1 543.56 2555.2
## <none> 543.09 2556.1
## - free.sulfur.dioxide 1 545.10 2558.8
## - pH 1 549.30 2568.7
## - chlorides 1 549.48 2569.1
## - total.sulfur.dioxide 1 550.99 2572.6
## - sulphates 1 561.51 2596.8
## - volatile.acidity 1 570.08 2616.1
## - alcohol 1 646.63 2777.3
##
## Step: AIC=2555.04
## .outcome ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 543.86 2553.9
## <none> 543.49 2555.0
## - free.sulfur.dioxide 1 545.83 2558.5
## - pH 1 549.69 2567.6
## - chlorides 1 550.66 2569.8
## - total.sulfur.dioxide 1 552.06 2573.1
## - sulphates 1 561.66 2595.1
## - volatile.acidity 1 575.28 2625.8
## - alcohol 1 648.47 2778.9
##
## Step: AIC=2553.92
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 543.86 2553.9
## - free.sulfur.dioxide 1 546.31 2557.7
## - pH 1 550.51 2567.5
## - chlorides 1 550.85 2568.3
## - total.sulfur.dioxide 1 552.12 2571.2
## - sulphates 1 561.80 2593.4
## - volatile.acidity 1 575.60 2624.5
## - alcohol 1 651.50 2782.9
## Start: AIC=3164.28
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 666.70 3163.0
## - fixed.acidity 1 666.80 3163.2
## - residual.sugar 1 666.91 3163.5
## - citric.acid 1 667.06 3163.8
## <none> 666.41 3164.3
## - free.sulfur.dioxide 1 668.10 3166.3
## - pH 1 668.37 3167.0
## - chlorides 1 674.80 3182.3
## - total.sulfur.dioxide 1 674.84 3182.4
## - sulphates 1 693.38 3225.7
## - volatile.acidity 1 700.03 3241.0
## - alcohol 1 712.08 3268.3
##
## Step: AIC=3162.96
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 666.81 3161.2
## - residual.sugar 1 666.93 3161.5
## - citric.acid 1 667.35 3162.5
## <none> 666.70 3163.0
## - free.sulfur.dioxide 1 668.53 3165.3
## - pH 1 671.02 3171.3
## - total.sulfur.dioxide 1 675.43 3181.8
## - chlorides 1 675.46 3181.8
## - sulphates 1 693.98 3225.1
## - volatile.acidity 1 701.70 3242.8
## - alcohol 1 786.37 3424.9
##
## Step: AIC=3161.22
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 667.06 3159.8
## - citric.acid 1 667.37 3160.6
## <none> 666.81 3161.2
## - free.sulfur.dioxide 1 668.71 3163.8
## - pH 1 673.87 3176.1
## - chlorides 1 676.75 3182.9
## - total.sulfur.dioxide 1 676.84 3183.1
## - sulphates 1 694.48 3224.2
## - volatile.acidity 1 703.04 3243.8
## - alcohol 1 787.44 3425.1
##
## Step: AIC=3159.84
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 667.54 3159.0
## <none> 667.06 3159.8
## - free.sulfur.dioxide 1 669.13 3162.8
## - pH 1 674.20 3174.9
## - total.sulfur.dioxide 1 676.89 3181.2
## - chlorides 1 676.89 3181.2
## - sulphates 1 694.51 3222.3
## - volatile.acidity 1 703.04 3241.8
## - alcohol 1 789.73 3427.8
##
## Step: AIC=3158.98
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 667.54 3159.0
## - free.sulfur.dioxide 1 669.93 3162.7
## - pH 1 674.61 3173.8
## - total.sulfur.dioxide 1 678.32 3182.6
## - chlorides 1 678.35 3182.7
## - sulphates 1 694.60 3220.5
## - volatile.acidity 1 709.85 3255.3
## - alcohol 1 792.02 3430.4
#model_stepwise
findCorrelation(
cor(df),
cutoff = 0.5,
verbose = TRUE,
names = TRUE
)
## Compare row 3 and column 1 with corr 0.672
## Means: 0.293 vs 0.19 so flagging column 3
## Compare row 1 and column 8 with corr 0.668
## Means: 0.245 vs 0.172 so flagging column 1
## Compare row 7 and column 6 with corr 0.668
## Means: 0.174 vs 0.169 so flagging column 7
## All correlations <= 0.5
## [1] "citric.acid" "fixed.acidity" "total.sulfur.dioxide"
ggcorrplot(correlation_df, hc.order = TRUE, type = "lower")
df_less_acid <- df %>%
select(-citric.acid, -fixed.acidity)
lm_less_acid <- lm(data = df_less_acid, quality ~ .)
summary(lm_less_acid)
##
## Call:
## lm(formula = quality ~ ., data = df_less_acid)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.66740 -0.37223 -0.04556 0.46264 2.03092
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.0575013 12.0089257 1.004 0.3155
## volatile.acidity -1.0127925 0.1009279 -10.035 < 2e-16 ***
## residual.sugar 0.0115046 0.0134606 0.855 0.3929
## chlorides -2.0490938 0.3992190 -5.133 3.21e-07 ***
## free.sulfur.dioxide 0.0048741 0.0021385 2.279 0.0228 *
## total.sulfur.dioxide -0.0035687 0.0006939 -5.143 3.03e-07 ***
## density -7.5668358 11.8648390 -0.638 0.5237
## pH -0.4919908 0.1210931 -4.063 5.08e-05 ***
## sulphates 0.9024434 0.1129657 7.989 2.60e-15 ***
## alcohol 0.2810022 0.0201992 13.912 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1589 degrees of freedom
## Multiple R-squared: 0.3598, Adjusted R-squared: 0.3562
## F-statistic: 99.22 on 9 and 1589 DF, p-value: < 2.2e-16
plot(df)
colnames(df)
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
cols = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol')
pre_proc_val <- preProcess(train[,cols], method = c("center", "scale"))
train[,cols] = predict(pre_proc_val, train[,cols])
test[,cols] = predict(pre_proc_val, test[,cols])
summary(train)
## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. :-2.1214 Min. :-2.29403 Min. :-1.38396 Min. :-1.19082
## 1st Qu.:-0.7040 1st Qu.:-0.72284 1st Qu.:-0.92625 1st Qu.:-0.46111
## Median :-0.2504 Median :-0.04947 Median :-0.06167 Median :-0.24219
## Mean : 0.0000 Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.5434 3rd Qu.: 0.62390 3rd Qu.: 0.80290 3rd Qu.: 0.04969
## Max. : 4.1152 Max. : 4.49577 Max. : 3.70176 Max. : 9.46298
## chlorides free.sulfur.dioxide total.sulfur.dioxide density
## Min. :-1.60030 Min. :-1.3925 Min. :-1.2082 Min. :-3.59039
## 1st Qu.:-0.36897 1st Qu.:-0.8179 1st Qu.:-0.7438 1st Qu.:-0.62763
## Median :-0.17790 Median :-0.2434 Median :-0.2794 Median : 0.01528
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.05563 3rd Qu.: 0.5227 3rd Qu.: 0.4636 3rd Qu.: 0.55640
## Max. :11.11635 Max. : 5.0235 Max. : 7.2123 Max. : 3.41736
## pH sulphates alcohol quality
## Min. :-3.65206 Min. :-1.9916 Min. :-1.9179 Min. :3.000
## 1st Qu.:-0.66269 1st Qu.:-0.6066 1st Qu.:-0.8757 1st Qu.:5.000
## Median :-0.02666 Median :-0.2452 Median :-0.2125 Median :6.000
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000 Mean :5.626
## 3rd Qu.: 0.54577 3rd Qu.: 0.4172 3rd Qu.: 0.6402 3rd Qu.:6.000
## Max. : 4.42559 Max. : 8.0652 Max. : 3.3879 Max. :8.000
#generic LM
lm_2 <- lm(quality ~ ., data = train)
summary(lm_2)
##
## Call:
## lm(formula = quality ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.69037 -0.36050 -0.04272 0.46333 2.09045
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.625559 0.019101 294.523 < 2e-16 ***
## fixed.acidity 0.016831 0.053411 0.315 0.752733
## volatile.acidity -0.220902 0.026177 -8.439 < 2e-16 ***
## citric.acid -0.068388 0.034985 -1.955 0.050861 .
## residual.sugar -0.008401 0.024615 -0.341 0.732932
## chlorides -0.095642 0.023189 -4.124 4.00e-05 ***
## free.sulfur.dioxide 0.057265 0.026656 2.148 0.031910 *
## total.sulfur.dioxide -0.095623 0.028346 -3.373 0.000768 ***
## density 0.025079 0.047489 0.528 0.597530
## pH -0.095685 0.035111 -2.725 0.006527 **
## sulphates 0.151876 0.022769 6.670 4.02e-11 ***
## alcohol 0.318605 0.032827 9.706 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6389 on 1107 degrees of freedom
## Multiple R-squared: 0.3671, Adjusted R-squared: 0.3609
## F-statistic: 58.38 on 11 and 1107 DF, p-value: < 2.2e-16
cols_reg = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol', 'quality')
dummies <- dummyVars(quality ~ ., data = df[,cols_reg])
train_dummies = predict(dummies, newdata = train[,cols_reg])
test_dummies = predict(dummies, newdata = test[,cols_reg])
print(dim(train_dummies)); print(dim(test_dummies))
## [1] 1119 11
## [1] 480 11
x = as.matrix(train_dummies)
y_train = train$quality
x_test = as.matrix(test_dummies)
y_test = test$quality
lambdas <- 10^seq(2, -3, by = -.1)
ridge_reg = glmnet(x, y_train, nlambda = 25, alpha = 0, family = 'gaussian', lambda = lambdas)
summary(ridge_reg)
## Length Class Mode
## a0 51 -none- numeric
## beta 561 dgCMatrix S4
## df 51 -none- numeric
## dim 2 -none- numeric
## lambda 51 -none- numeric
## dev.ratio 51 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numeric
cv_ridge <- cv.glmnet(x, y_train, alpha = 0, lambda = lambdas)
optimal_lambda <- cv_ridge$lambda.min
optimal_lambda
## [1] 0.01995262
# Compute R^2 from true and predicted values
eval_results <- function(true, predicted, df) {
SSE <- sum((predicted - true)^2)
SST <- sum((true - mean(true))^2)
R_square <- 1 - SSE / SST
RMSE = sqrt(SSE/nrow(df))
# Model performance metrics
data.frame(
RMSE = RMSE,
Rsquare = R_square
)
}
# Prediction and evaluation on train data
predictions_train <- predict(ridge_reg, s = optimal_lambda, newx = x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6357245 0.3667089
# Prediction and evaluation on test data
predictions_test <- predict(ridge_reg, s = optimal_lambda, newx = x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6710556 0.3402934
lambdas <- 10^seq(2, -3, by = -.1)
# Setting alpha = 1 implements lasso regression
lasso_reg <- cv.glmnet(x, y_train, alpha = 1, lambda = lambdas, standardize = TRUE, nfolds = 5)
# Best
lambda_best <- lasso_reg$lambda.min
lambda_best
## [1] 0.006309573
lasso_model <- glmnet(x, y_train, alpha = 1, lambda = lambda_best, standardize = TRUE)
predictions_train <- predict(lasso_model, s = lambda_best, newx = x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6362121 0.3657369
predictions_test <- predict(lasso_model, s = lambda_best, newx = x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6696633 0.343028
# Set training control
train_cont <- trainControl(method = "repeatedcv",
number = 10,
repeats = 5,
search = "random",
verboseIter = TRUE)
# Train the model
elastic_reg <- train(quality ~ .,
data = train,
method = "glmnet",
preProcess = c("center", "scale"),
tuneLength = 10,
trControl = train_cont)
## + Fold01.Rep1: alpha=0.30285, lambda=0.004666
## - Fold01.Rep1: alpha=0.30285, lambda=0.004666
## + Fold01.Rep1: alpha=0.02355, lambda=0.061703
## - Fold01.Rep1: alpha=0.02355, lambda=0.061703
## + Fold01.Rep1: alpha=0.32050, lambda=0.005575
## - Fold01.Rep1: alpha=0.32050, lambda=0.005575
## + Fold01.Rep1: alpha=0.03179, lambda=0.019563
## - Fold01.Rep1: alpha=0.03179, lambda=0.019563
## + Fold01.Rep1: alpha=0.55008, lambda=0.600447
## - Fold01.Rep1: alpha=0.55008, lambda=0.600447
## + Fold01.Rep1: alpha=0.71987, lambda=0.017336
## - Fold01.Rep1: alpha=0.71987, lambda=0.017336
## + Fold01.Rep1: alpha=0.16961, lambda=0.086625
## - Fold01.Rep1: alpha=0.16961, lambda=0.086625
## + Fold01.Rep1: alpha=0.61948, lambda=0.011854
## - Fold01.Rep1: alpha=0.61948, lambda=0.011854
## + Fold01.Rep1: alpha=0.18579, lambda=0.002510
## - Fold01.Rep1: alpha=0.18579, lambda=0.002510
## + Fold01.Rep1: alpha=0.36092, lambda=0.018533
## - Fold01.Rep1: alpha=0.36092, lambda=0.018533
## + Fold02.Rep1: alpha=0.30285, lambda=0.004666
## - Fold02.Rep1: alpha=0.30285, lambda=0.004666
## + Fold02.Rep1: alpha=0.02355, lambda=0.061703
## - Fold02.Rep1: alpha=0.02355, lambda=0.061703
## + Fold02.Rep1: alpha=0.32050, lambda=0.005575
## - Fold02.Rep1: alpha=0.32050, lambda=0.005575
## + Fold02.Rep1: alpha=0.03179, lambda=0.019563
## - Fold02.Rep1: alpha=0.03179, lambda=0.019563
## + Fold02.Rep1: alpha=0.55008, lambda=0.600447
## - Fold02.Rep1: alpha=0.55008, lambda=0.600447
## + Fold02.Rep1: alpha=0.71987, lambda=0.017336
## - Fold02.Rep1: alpha=0.71987, lambda=0.017336
## + Fold02.Rep1: alpha=0.16961, lambda=0.086625
## - Fold02.Rep1: alpha=0.16961, lambda=0.086625
## + Fold02.Rep1: alpha=0.61948, lambda=0.011854
## - Fold02.Rep1: alpha=0.61948, lambda=0.011854
## + Fold02.Rep1: alpha=0.18579, lambda=0.002510
## - Fold02.Rep1: alpha=0.18579, lambda=0.002510
## + Fold02.Rep1: alpha=0.36092, lambda=0.018533
## - Fold02.Rep1: alpha=0.36092, lambda=0.018533
## + Fold03.Rep1: alpha=0.30285, lambda=0.004666
## - Fold03.Rep1: alpha=0.30285, lambda=0.004666
## + Fold03.Rep1: alpha=0.02355, lambda=0.061703
## - Fold03.Rep1: alpha=0.02355, lambda=0.061703
## + Fold03.Rep1: alpha=0.32050, lambda=0.005575
## - Fold03.Rep1: alpha=0.32050, lambda=0.005575
## + Fold03.Rep1: alpha=0.03179, lambda=0.019563
## - Fold03.Rep1: alpha=0.03179, lambda=0.019563
## + Fold03.Rep1: alpha=0.55008, lambda=0.600447
## - Fold03.Rep1: alpha=0.55008, lambda=0.600447
## + Fold03.Rep1: alpha=0.71987, lambda=0.017336
## - Fold03.Rep1: alpha=0.71987, lambda=0.017336
## + Fold03.Rep1: alpha=0.16961, lambda=0.086625
## - Fold03.Rep1: alpha=0.16961, lambda=0.086625
## + Fold03.Rep1: alpha=0.61948, lambda=0.011854
## - Fold03.Rep1: alpha=0.61948, lambda=0.011854
## + Fold03.Rep1: alpha=0.18579, lambda=0.002510
## - Fold03.Rep1: alpha=0.18579, lambda=0.002510
## + Fold03.Rep1: alpha=0.36092, lambda=0.018533
## - Fold03.Rep1: alpha=0.36092, lambda=0.018533
## + Fold04.Rep1: alpha=0.30285, lambda=0.004666
## - Fold04.Rep1: alpha=0.30285, lambda=0.004666
## + Fold04.Rep1: alpha=0.02355, lambda=0.061703
## - Fold04.Rep1: alpha=0.02355, lambda=0.061703
## + Fold04.Rep1: alpha=0.32050, lambda=0.005575
## - Fold04.Rep1: alpha=0.32050, lambda=0.005575
## + Fold04.Rep1: alpha=0.03179, lambda=0.019563
## - Fold04.Rep1: alpha=0.03179, lambda=0.019563
## + Fold04.Rep1: alpha=0.55008, lambda=0.600447
## - Fold04.Rep1: alpha=0.55008, lambda=0.600447
## + Fold04.Rep1: alpha=0.71987, lambda=0.017336
## - Fold04.Rep1: alpha=0.71987, lambda=0.017336
## + Fold04.Rep1: alpha=0.16961, lambda=0.086625
## - Fold04.Rep1: alpha=0.16961, lambda=0.086625
## + Fold04.Rep1: alpha=0.61948, lambda=0.011854
## - Fold04.Rep1: alpha=0.61948, lambda=0.011854
## + Fold04.Rep1: alpha=0.18579, lambda=0.002510
## - Fold04.Rep1: alpha=0.18579, lambda=0.002510
## + Fold04.Rep1: alpha=0.36092, lambda=0.018533
## - Fold04.Rep1: alpha=0.36092, lambda=0.018533
## + Fold05.Rep1: alpha=0.30285, lambda=0.004666
## - Fold05.Rep1: alpha=0.30285, lambda=0.004666
## + Fold05.Rep1: alpha=0.02355, lambda=0.061703
## - Fold05.Rep1: alpha=0.02355, lambda=0.061703
## + Fold05.Rep1: alpha=0.32050, lambda=0.005575
## - Fold05.Rep1: alpha=0.32050, lambda=0.005575
## + Fold05.Rep1: alpha=0.03179, lambda=0.019563
## - Fold05.Rep1: alpha=0.03179, lambda=0.019563
## + Fold05.Rep1: alpha=0.55008, lambda=0.600447
## - Fold05.Rep1: alpha=0.55008, lambda=0.600447
## + Fold05.Rep1: alpha=0.71987, lambda=0.017336
## - Fold05.Rep1: alpha=0.71987, lambda=0.017336
## + Fold05.Rep1: alpha=0.16961, lambda=0.086625
## - Fold05.Rep1: alpha=0.16961, lambda=0.086625
## + Fold05.Rep1: alpha=0.61948, lambda=0.011854
## - Fold05.Rep1: alpha=0.61948, lambda=0.011854
## + Fold05.Rep1: alpha=0.18579, lambda=0.002510
## - Fold05.Rep1: alpha=0.18579, lambda=0.002510
## + Fold05.Rep1: alpha=0.36092, lambda=0.018533
## - Fold05.Rep1: alpha=0.36092, lambda=0.018533
## + Fold06.Rep1: alpha=0.30285, lambda=0.004666
## - Fold06.Rep1: alpha=0.30285, lambda=0.004666
## + Fold06.Rep1: alpha=0.02355, lambda=0.061703
## - Fold06.Rep1: alpha=0.02355, lambda=0.061703
## + Fold06.Rep1: alpha=0.32050, lambda=0.005575
## - Fold06.Rep1: alpha=0.32050, lambda=0.005575
## + Fold06.Rep1: alpha=0.03179, lambda=0.019563
## - Fold06.Rep1: alpha=0.03179, lambda=0.019563
## + Fold06.Rep1: alpha=0.55008, lambda=0.600447
## - Fold06.Rep1: alpha=0.55008, lambda=0.600447
## + Fold06.Rep1: alpha=0.71987, lambda=0.017336
## - Fold06.Rep1: alpha=0.71987, lambda=0.017336
## + Fold06.Rep1: alpha=0.16961, lambda=0.086625
## - Fold06.Rep1: alpha=0.16961, lambda=0.086625
## + Fold06.Rep1: alpha=0.61948, lambda=0.011854
## - Fold06.Rep1: alpha=0.61948, lambda=0.011854
## + Fold06.Rep1: alpha=0.18579, lambda=0.002510
## - Fold06.Rep1: alpha=0.18579, lambda=0.002510
## + Fold06.Rep1: alpha=0.36092, lambda=0.018533
## - Fold06.Rep1: alpha=0.36092, lambda=0.018533
## + Fold07.Rep1: alpha=0.30285, lambda=0.004666
## - Fold07.Rep1: alpha=0.30285, lambda=0.004666
## + Fold07.Rep1: alpha=0.02355, lambda=0.061703
## - Fold07.Rep1: alpha=0.02355, lambda=0.061703
## + Fold07.Rep1: alpha=0.32050, lambda=0.005575
## - Fold07.Rep1: alpha=0.32050, lambda=0.005575
## + Fold07.Rep1: alpha=0.03179, lambda=0.019563
## - Fold07.Rep1: alpha=0.03179, lambda=0.019563
## + Fold07.Rep1: alpha=0.55008, lambda=0.600447
## - Fold07.Rep1: alpha=0.55008, lambda=0.600447
## + Fold07.Rep1: alpha=0.71987, lambda=0.017336
## - Fold07.Rep1: alpha=0.71987, lambda=0.017336
## + Fold07.Rep1: alpha=0.16961, lambda=0.086625
## - Fold07.Rep1: alpha=0.16961, lambda=0.086625
## + Fold07.Rep1: alpha=0.61948, lambda=0.011854
## - Fold07.Rep1: alpha=0.61948, lambda=0.011854
## + Fold07.Rep1: alpha=0.18579, lambda=0.002510
## - Fold07.Rep1: alpha=0.18579, lambda=0.002510
## + Fold07.Rep1: alpha=0.36092, lambda=0.018533
## - Fold07.Rep1: alpha=0.36092, lambda=0.018533
## + Fold08.Rep1: alpha=0.30285, lambda=0.004666
## - Fold08.Rep1: alpha=0.30285, lambda=0.004666
## + Fold08.Rep1: alpha=0.02355, lambda=0.061703
## - Fold08.Rep1: alpha=0.02355, lambda=0.061703
## + Fold08.Rep1: alpha=0.32050, lambda=0.005575
## - Fold08.Rep1: alpha=0.32050, lambda=0.005575
## + Fold08.Rep1: alpha=0.03179, lambda=0.019563
## - Fold08.Rep1: alpha=0.03179, lambda=0.019563
## + Fold08.Rep1: alpha=0.55008, lambda=0.600447
## - Fold08.Rep1: alpha=0.55008, lambda=0.600447
## + Fold08.Rep1: alpha=0.71987, lambda=0.017336
## - Fold08.Rep1: alpha=0.71987, lambda=0.017336
## + Fold08.Rep1: alpha=0.16961, lambda=0.086625
## - Fold08.Rep1: alpha=0.16961, lambda=0.086625
## + Fold08.Rep1: alpha=0.61948, lambda=0.011854
## - Fold08.Rep1: alpha=0.61948, lambda=0.011854
## + Fold08.Rep1: alpha=0.18579, lambda=0.002510
## - Fold08.Rep1: alpha=0.18579, lambda=0.002510
## + Fold08.Rep1: alpha=0.36092, lambda=0.018533
## - Fold08.Rep1: alpha=0.36092, lambda=0.018533
## + Fold09.Rep1: alpha=0.30285, lambda=0.004666
## - Fold09.Rep1: alpha=0.30285, lambda=0.004666
## + Fold09.Rep1: alpha=0.02355, lambda=0.061703
## - Fold09.Rep1: alpha=0.02355, lambda=0.061703
## + Fold09.Rep1: alpha=0.32050, lambda=0.005575
## - Fold09.Rep1: alpha=0.32050, lambda=0.005575
## + Fold09.Rep1: alpha=0.03179, lambda=0.019563
## - Fold09.Rep1: alpha=0.03179, lambda=0.019563
## + Fold09.Rep1: alpha=0.55008, lambda=0.600447
## - Fold09.Rep1: alpha=0.55008, lambda=0.600447
## + Fold09.Rep1: alpha=0.71987, lambda=0.017336
## - Fold09.Rep1: alpha=0.71987, lambda=0.017336
## + Fold09.Rep1: alpha=0.16961, lambda=0.086625
## - Fold09.Rep1: alpha=0.16961, lambda=0.086625
## + Fold09.Rep1: alpha=0.61948, lambda=0.011854
## - Fold09.Rep1: alpha=0.61948, lambda=0.011854
## + Fold09.Rep1: alpha=0.18579, lambda=0.002510
## - Fold09.Rep1: alpha=0.18579, lambda=0.002510
## + Fold09.Rep1: alpha=0.36092, lambda=0.018533
## - Fold09.Rep1: alpha=0.36092, lambda=0.018533
## + Fold10.Rep1: alpha=0.30285, lambda=0.004666
## - Fold10.Rep1: alpha=0.30285, lambda=0.004666
## + Fold10.Rep1: alpha=0.02355, lambda=0.061703
## - Fold10.Rep1: alpha=0.02355, lambda=0.061703
## + Fold10.Rep1: alpha=0.32050, lambda=0.005575
## - Fold10.Rep1: alpha=0.32050, lambda=0.005575
## + Fold10.Rep1: alpha=0.03179, lambda=0.019563
## - Fold10.Rep1: alpha=0.03179, lambda=0.019563
## + Fold10.Rep1: alpha=0.55008, lambda=0.600447
## - Fold10.Rep1: alpha=0.55008, lambda=0.600447
## + Fold10.Rep1: alpha=0.71987, lambda=0.017336
## - Fold10.Rep1: alpha=0.71987, lambda=0.017336
## + Fold10.Rep1: alpha=0.16961, lambda=0.086625
## - Fold10.Rep1: alpha=0.16961, lambda=0.086625
## + Fold10.Rep1: alpha=0.61948, lambda=0.011854
## - Fold10.Rep1: alpha=0.61948, lambda=0.011854
## + Fold10.Rep1: alpha=0.18579, lambda=0.002510
## - Fold10.Rep1: alpha=0.18579, lambda=0.002510
## + Fold10.Rep1: alpha=0.36092, lambda=0.018533
## - Fold10.Rep1: alpha=0.36092, lambda=0.018533
## + Fold01.Rep2: alpha=0.30285, lambda=0.004666
## - Fold01.Rep2: alpha=0.30285, lambda=0.004666
## + Fold01.Rep2: alpha=0.02355, lambda=0.061703
## - Fold01.Rep2: alpha=0.02355, lambda=0.061703
## + Fold01.Rep2: alpha=0.32050, lambda=0.005575
## - Fold01.Rep2: alpha=0.32050, lambda=0.005575
## + Fold01.Rep2: alpha=0.03179, lambda=0.019563
## - Fold01.Rep2: alpha=0.03179, lambda=0.019563
## + Fold01.Rep2: alpha=0.55008, lambda=0.600447
## - Fold01.Rep2: alpha=0.55008, lambda=0.600447
## + Fold01.Rep2: alpha=0.71987, lambda=0.017336
## - Fold01.Rep2: alpha=0.71987, lambda=0.017336
## + Fold01.Rep2: alpha=0.16961, lambda=0.086625
## - Fold01.Rep2: alpha=0.16961, lambda=0.086625
## + Fold01.Rep2: alpha=0.61948, lambda=0.011854
## - Fold01.Rep2: alpha=0.61948, lambda=0.011854
## + Fold01.Rep2: alpha=0.18579, lambda=0.002510
## - Fold01.Rep2: alpha=0.18579, lambda=0.002510
## + Fold01.Rep2: alpha=0.36092, lambda=0.018533
## - Fold01.Rep2: alpha=0.36092, lambda=0.018533
## + Fold02.Rep2: alpha=0.30285, lambda=0.004666
## - Fold02.Rep2: alpha=0.30285, lambda=0.004666
## + Fold02.Rep2: alpha=0.02355, lambda=0.061703
## - Fold02.Rep2: alpha=0.02355, lambda=0.061703
## + Fold02.Rep2: alpha=0.32050, lambda=0.005575
## - Fold02.Rep2: alpha=0.32050, lambda=0.005575
## + Fold02.Rep2: alpha=0.03179, lambda=0.019563
## - Fold02.Rep2: alpha=0.03179, lambda=0.019563
## + Fold02.Rep2: alpha=0.55008, lambda=0.600447
## - Fold02.Rep2: alpha=0.55008, lambda=0.600447
## + Fold02.Rep2: alpha=0.71987, lambda=0.017336
## - Fold02.Rep2: alpha=0.71987, lambda=0.017336
## + Fold02.Rep2: alpha=0.16961, lambda=0.086625
## - Fold02.Rep2: alpha=0.16961, lambda=0.086625
## + Fold02.Rep2: alpha=0.61948, lambda=0.011854
## - Fold02.Rep2: alpha=0.61948, lambda=0.011854
## + Fold02.Rep2: alpha=0.18579, lambda=0.002510
## - Fold02.Rep2: alpha=0.18579, lambda=0.002510
## + Fold02.Rep2: alpha=0.36092, lambda=0.018533
## - Fold02.Rep2: alpha=0.36092, lambda=0.018533
## + Fold03.Rep2: alpha=0.30285, lambda=0.004666
## - Fold03.Rep2: alpha=0.30285, lambda=0.004666
## + Fold03.Rep2: alpha=0.02355, lambda=0.061703
## - Fold03.Rep2: alpha=0.02355, lambda=0.061703
## + Fold03.Rep2: alpha=0.32050, lambda=0.005575
## - Fold03.Rep2: alpha=0.32050, lambda=0.005575
## + Fold03.Rep2: alpha=0.03179, lambda=0.019563
## - Fold03.Rep2: alpha=0.03179, lambda=0.019563
## + Fold03.Rep2: alpha=0.55008, lambda=0.600447
## - Fold03.Rep2: alpha=0.55008, lambda=0.600447
## + Fold03.Rep2: alpha=0.71987, lambda=0.017336
## - Fold03.Rep2: alpha=0.71987, lambda=0.017336
## + Fold03.Rep2: alpha=0.16961, lambda=0.086625
## - Fold03.Rep2: alpha=0.16961, lambda=0.086625
## + Fold03.Rep2: alpha=0.61948, lambda=0.011854
## - Fold03.Rep2: alpha=0.61948, lambda=0.011854
## + Fold03.Rep2: alpha=0.18579, lambda=0.002510
## - Fold03.Rep2: alpha=0.18579, lambda=0.002510
## + Fold03.Rep2: alpha=0.36092, lambda=0.018533
## - Fold03.Rep2: alpha=0.36092, lambda=0.018533
## + Fold04.Rep2: alpha=0.30285, lambda=0.004666
## - Fold04.Rep2: alpha=0.30285, lambda=0.004666
## + Fold04.Rep2: alpha=0.02355, lambda=0.061703
## - Fold04.Rep2: alpha=0.02355, lambda=0.061703
## + Fold04.Rep2: alpha=0.32050, lambda=0.005575
## - Fold04.Rep2: alpha=0.32050, lambda=0.005575
## + Fold04.Rep2: alpha=0.03179, lambda=0.019563
## - Fold04.Rep2: alpha=0.03179, lambda=0.019563
## + Fold04.Rep2: alpha=0.55008, lambda=0.600447
## - Fold04.Rep2: alpha=0.55008, lambda=0.600447
## + Fold04.Rep2: alpha=0.71987, lambda=0.017336
## - Fold04.Rep2: alpha=0.71987, lambda=0.017336
## + Fold04.Rep2: alpha=0.16961, lambda=0.086625
## - Fold04.Rep2: alpha=0.16961, lambda=0.086625
## + Fold04.Rep2: alpha=0.61948, lambda=0.011854
## - Fold04.Rep2: alpha=0.61948, lambda=0.011854
## + Fold04.Rep2: alpha=0.18579, lambda=0.002510
## - Fold04.Rep2: alpha=0.18579, lambda=0.002510
## + Fold04.Rep2: alpha=0.36092, lambda=0.018533
## - Fold04.Rep2: alpha=0.36092, lambda=0.018533
## + Fold05.Rep2: alpha=0.30285, lambda=0.004666
## - Fold05.Rep2: alpha=0.30285, lambda=0.004666
## + Fold05.Rep2: alpha=0.02355, lambda=0.061703
## - Fold05.Rep2: alpha=0.02355, lambda=0.061703
## + Fold05.Rep2: alpha=0.32050, lambda=0.005575
## - Fold05.Rep2: alpha=0.32050, lambda=0.005575
## + Fold05.Rep2: alpha=0.03179, lambda=0.019563
## - Fold05.Rep2: alpha=0.03179, lambda=0.019563
## + Fold05.Rep2: alpha=0.55008, lambda=0.600447
## - Fold05.Rep2: alpha=0.55008, lambda=0.600447
## + Fold05.Rep2: alpha=0.71987, lambda=0.017336
## - Fold05.Rep2: alpha=0.71987, lambda=0.017336
## + Fold05.Rep2: alpha=0.16961, lambda=0.086625
## - Fold05.Rep2: alpha=0.16961, lambda=0.086625
## + Fold05.Rep2: alpha=0.61948, lambda=0.011854
## - Fold05.Rep2: alpha=0.61948, lambda=0.011854
## + Fold05.Rep2: alpha=0.18579, lambda=0.002510
## - Fold05.Rep2: alpha=0.18579, lambda=0.002510
## + Fold05.Rep2: alpha=0.36092, lambda=0.018533
## - Fold05.Rep2: alpha=0.36092, lambda=0.018533
## + Fold06.Rep2: alpha=0.30285, lambda=0.004666
## - Fold06.Rep2: alpha=0.30285, lambda=0.004666
## + Fold06.Rep2: alpha=0.02355, lambda=0.061703
## - Fold06.Rep2: alpha=0.02355, lambda=0.061703
## + Fold06.Rep2: alpha=0.32050, lambda=0.005575
## - Fold06.Rep2: alpha=0.32050, lambda=0.005575
## + Fold06.Rep2: alpha=0.03179, lambda=0.019563
## - Fold06.Rep2: alpha=0.03179, lambda=0.019563
## + Fold06.Rep2: alpha=0.55008, lambda=0.600447
## - Fold06.Rep2: alpha=0.55008, lambda=0.600447
## + Fold06.Rep2: alpha=0.71987, lambda=0.017336
## - Fold06.Rep2: alpha=0.71987, lambda=0.017336
## + Fold06.Rep2: alpha=0.16961, lambda=0.086625
## - Fold06.Rep2: alpha=0.16961, lambda=0.086625
## + Fold06.Rep2: alpha=0.61948, lambda=0.011854
## - Fold06.Rep2: alpha=0.61948, lambda=0.011854
## + Fold06.Rep2: alpha=0.18579, lambda=0.002510
## - Fold06.Rep2: alpha=0.18579, lambda=0.002510
## + Fold06.Rep2: alpha=0.36092, lambda=0.018533
## - Fold06.Rep2: alpha=0.36092, lambda=0.018533
## + Fold07.Rep2: alpha=0.30285, lambda=0.004666
## - Fold07.Rep2: alpha=0.30285, lambda=0.004666
## + Fold07.Rep2: alpha=0.02355, lambda=0.061703
## - Fold07.Rep2: alpha=0.02355, lambda=0.061703
## + Fold07.Rep2: alpha=0.32050, lambda=0.005575
## - Fold07.Rep2: alpha=0.32050, lambda=0.005575
## + Fold07.Rep2: alpha=0.03179, lambda=0.019563
## - Fold07.Rep2: alpha=0.03179, lambda=0.019563
## + Fold07.Rep2: alpha=0.55008, lambda=0.600447
## - Fold07.Rep2: alpha=0.55008, lambda=0.600447
## + Fold07.Rep2: alpha=0.71987, lambda=0.017336
## - Fold07.Rep2: alpha=0.71987, lambda=0.017336
## + Fold07.Rep2: alpha=0.16961, lambda=0.086625
## - Fold07.Rep2: alpha=0.16961, lambda=0.086625
## + Fold07.Rep2: alpha=0.61948, lambda=0.011854
## - Fold07.Rep2: alpha=0.61948, lambda=0.011854
## + Fold07.Rep2: alpha=0.18579, lambda=0.002510
## - Fold07.Rep2: alpha=0.18579, lambda=0.002510
## + Fold07.Rep2: alpha=0.36092, lambda=0.018533
## - Fold07.Rep2: alpha=0.36092, lambda=0.018533
## + Fold08.Rep2: alpha=0.30285, lambda=0.004666
## - Fold08.Rep2: alpha=0.30285, lambda=0.004666
## + Fold08.Rep2: alpha=0.02355, lambda=0.061703
## - Fold08.Rep2: alpha=0.02355, lambda=0.061703
## + Fold08.Rep2: alpha=0.32050, lambda=0.005575
## - Fold08.Rep2: alpha=0.32050, lambda=0.005575
## + Fold08.Rep2: alpha=0.03179, lambda=0.019563
## - Fold08.Rep2: alpha=0.03179, lambda=0.019563
## + Fold08.Rep2: alpha=0.55008, lambda=0.600447
## - Fold08.Rep2: alpha=0.55008, lambda=0.600447
## + Fold08.Rep2: alpha=0.71987, lambda=0.017336
## - Fold08.Rep2: alpha=0.71987, lambda=0.017336
## + Fold08.Rep2: alpha=0.16961, lambda=0.086625
## - Fold08.Rep2: alpha=0.16961, lambda=0.086625
## + Fold08.Rep2: alpha=0.61948, lambda=0.011854
## - Fold08.Rep2: alpha=0.61948, lambda=0.011854
## + Fold08.Rep2: alpha=0.18579, lambda=0.002510
## - Fold08.Rep2: alpha=0.18579, lambda=0.002510
## + Fold08.Rep2: alpha=0.36092, lambda=0.018533
## - Fold08.Rep2: alpha=0.36092, lambda=0.018533
## + Fold09.Rep2: alpha=0.30285, lambda=0.004666
## - Fold09.Rep2: alpha=0.30285, lambda=0.004666
## + Fold09.Rep2: alpha=0.02355, lambda=0.061703
## - Fold09.Rep2: alpha=0.02355, lambda=0.061703
## + Fold09.Rep2: alpha=0.32050, lambda=0.005575
## - Fold09.Rep2: alpha=0.32050, lambda=0.005575
## + Fold09.Rep2: alpha=0.03179, lambda=0.019563
## - Fold09.Rep2: alpha=0.03179, lambda=0.019563
## + Fold09.Rep2: alpha=0.55008, lambda=0.600447
## - Fold09.Rep2: alpha=0.55008, lambda=0.600447
## + Fold09.Rep2: alpha=0.71987, lambda=0.017336
## - Fold09.Rep2: alpha=0.71987, lambda=0.017336
## + Fold09.Rep2: alpha=0.16961, lambda=0.086625
## - Fold09.Rep2: alpha=0.16961, lambda=0.086625
## + Fold09.Rep2: alpha=0.61948, lambda=0.011854
## - Fold09.Rep2: alpha=0.61948, lambda=0.011854
## + Fold09.Rep2: alpha=0.18579, lambda=0.002510
## - Fold09.Rep2: alpha=0.18579, lambda=0.002510
## + Fold09.Rep2: alpha=0.36092, lambda=0.018533
## - Fold09.Rep2: alpha=0.36092, lambda=0.018533
## + Fold10.Rep2: alpha=0.30285, lambda=0.004666
## - Fold10.Rep2: alpha=0.30285, lambda=0.004666
## + Fold10.Rep2: alpha=0.02355, lambda=0.061703
## - Fold10.Rep2: alpha=0.02355, lambda=0.061703
## + Fold10.Rep2: alpha=0.32050, lambda=0.005575
## - Fold10.Rep2: alpha=0.32050, lambda=0.005575
## + Fold10.Rep2: alpha=0.03179, lambda=0.019563
## - Fold10.Rep2: alpha=0.03179, lambda=0.019563
## + Fold10.Rep2: alpha=0.55008, lambda=0.600447
## - Fold10.Rep2: alpha=0.55008, lambda=0.600447
## + Fold10.Rep2: alpha=0.71987, lambda=0.017336
## - Fold10.Rep2: alpha=0.71987, lambda=0.017336
## + Fold10.Rep2: alpha=0.16961, lambda=0.086625
## - Fold10.Rep2: alpha=0.16961, lambda=0.086625
## + Fold10.Rep2: alpha=0.61948, lambda=0.011854
## - Fold10.Rep2: alpha=0.61948, lambda=0.011854
## + Fold10.Rep2: alpha=0.18579, lambda=0.002510
## - Fold10.Rep2: alpha=0.18579, lambda=0.002510
## + Fold10.Rep2: alpha=0.36092, lambda=0.018533
## - Fold10.Rep2: alpha=0.36092, lambda=0.018533
## + Fold01.Rep3: alpha=0.30285, lambda=0.004666
## - Fold01.Rep3: alpha=0.30285, lambda=0.004666
## + Fold01.Rep3: alpha=0.02355, lambda=0.061703
## - Fold01.Rep3: alpha=0.02355, lambda=0.061703
## + Fold01.Rep3: alpha=0.32050, lambda=0.005575
## - Fold01.Rep3: alpha=0.32050, lambda=0.005575
## + Fold01.Rep3: alpha=0.03179, lambda=0.019563
## - Fold01.Rep3: alpha=0.03179, lambda=0.019563
## + Fold01.Rep3: alpha=0.55008, lambda=0.600447
## - Fold01.Rep3: alpha=0.55008, lambda=0.600447
## + Fold01.Rep3: alpha=0.71987, lambda=0.017336
## - Fold01.Rep3: alpha=0.71987, lambda=0.017336
## + Fold01.Rep3: alpha=0.16961, lambda=0.086625
## - Fold01.Rep3: alpha=0.16961, lambda=0.086625
## + Fold01.Rep3: alpha=0.61948, lambda=0.011854
## - Fold01.Rep3: alpha=0.61948, lambda=0.011854
## + Fold01.Rep3: alpha=0.18579, lambda=0.002510
## - Fold01.Rep3: alpha=0.18579, lambda=0.002510
## + Fold01.Rep3: alpha=0.36092, lambda=0.018533
## - Fold01.Rep3: alpha=0.36092, lambda=0.018533
## + Fold02.Rep3: alpha=0.30285, lambda=0.004666
## - Fold02.Rep3: alpha=0.30285, lambda=0.004666
## + Fold02.Rep3: alpha=0.02355, lambda=0.061703
## - Fold02.Rep3: alpha=0.02355, lambda=0.061703
## + Fold02.Rep3: alpha=0.32050, lambda=0.005575
## - Fold02.Rep3: alpha=0.32050, lambda=0.005575
## + Fold02.Rep3: alpha=0.03179, lambda=0.019563
## - Fold02.Rep3: alpha=0.03179, lambda=0.019563
## + Fold02.Rep3: alpha=0.55008, lambda=0.600447
## - Fold02.Rep3: alpha=0.55008, lambda=0.600447
## + Fold02.Rep3: alpha=0.71987, lambda=0.017336
## - Fold02.Rep3: alpha=0.71987, lambda=0.017336
## + Fold02.Rep3: alpha=0.16961, lambda=0.086625
## - Fold02.Rep3: alpha=0.16961, lambda=0.086625
## + Fold02.Rep3: alpha=0.61948, lambda=0.011854
## - Fold02.Rep3: alpha=0.61948, lambda=0.011854
## + Fold02.Rep3: alpha=0.18579, lambda=0.002510
## - Fold02.Rep3: alpha=0.18579, lambda=0.002510
## + Fold02.Rep3: alpha=0.36092, lambda=0.018533
## - Fold02.Rep3: alpha=0.36092, lambda=0.018533
## + Fold03.Rep3: alpha=0.30285, lambda=0.004666
## - Fold03.Rep3: alpha=0.30285, lambda=0.004666
## + Fold03.Rep3: alpha=0.02355, lambda=0.061703
## - Fold03.Rep3: alpha=0.02355, lambda=0.061703
## + Fold03.Rep3: alpha=0.32050, lambda=0.005575
## - Fold03.Rep3: alpha=0.32050, lambda=0.005575
## + Fold03.Rep3: alpha=0.03179, lambda=0.019563
## - Fold03.Rep3: alpha=0.03179, lambda=0.019563
## + Fold03.Rep3: alpha=0.55008, lambda=0.600447
## - Fold03.Rep3: alpha=0.55008, lambda=0.600447
## + Fold03.Rep3: alpha=0.71987, lambda=0.017336
## - Fold03.Rep3: alpha=0.71987, lambda=0.017336
## + Fold03.Rep3: alpha=0.16961, lambda=0.086625
## - Fold03.Rep3: alpha=0.16961, lambda=0.086625
## + Fold03.Rep3: alpha=0.61948, lambda=0.011854
## - Fold03.Rep3: alpha=0.61948, lambda=0.011854
## + Fold03.Rep3: alpha=0.18579, lambda=0.002510
## - Fold03.Rep3: alpha=0.18579, lambda=0.002510
## + Fold03.Rep3: alpha=0.36092, lambda=0.018533
## - Fold03.Rep3: alpha=0.36092, lambda=0.018533
## + Fold04.Rep3: alpha=0.30285, lambda=0.004666
## - Fold04.Rep3: alpha=0.30285, lambda=0.004666
## + Fold04.Rep3: alpha=0.02355, lambda=0.061703
## - Fold04.Rep3: alpha=0.02355, lambda=0.061703
## + Fold04.Rep3: alpha=0.32050, lambda=0.005575
## - Fold04.Rep3: alpha=0.32050, lambda=0.005575
## + Fold04.Rep3: alpha=0.03179, lambda=0.019563
## - Fold04.Rep3: alpha=0.03179, lambda=0.019563
## + Fold04.Rep3: alpha=0.55008, lambda=0.600447
## - Fold04.Rep3: alpha=0.55008, lambda=0.600447
## + Fold04.Rep3: alpha=0.71987, lambda=0.017336
## - Fold04.Rep3: alpha=0.71987, lambda=0.017336
## + Fold04.Rep3: alpha=0.16961, lambda=0.086625
## - Fold04.Rep3: alpha=0.16961, lambda=0.086625
## + Fold04.Rep3: alpha=0.61948, lambda=0.011854
## - Fold04.Rep3: alpha=0.61948, lambda=0.011854
## + Fold04.Rep3: alpha=0.18579, lambda=0.002510
## - Fold04.Rep3: alpha=0.18579, lambda=0.002510
## + Fold04.Rep3: alpha=0.36092, lambda=0.018533
## - Fold04.Rep3: alpha=0.36092, lambda=0.018533
## + Fold05.Rep3: alpha=0.30285, lambda=0.004666
## - Fold05.Rep3: alpha=0.30285, lambda=0.004666
## + Fold05.Rep3: alpha=0.02355, lambda=0.061703
## - Fold05.Rep3: alpha=0.02355, lambda=0.061703
## + Fold05.Rep3: alpha=0.32050, lambda=0.005575
## - Fold05.Rep3: alpha=0.32050, lambda=0.005575
## + Fold05.Rep3: alpha=0.03179, lambda=0.019563
## - Fold05.Rep3: alpha=0.03179, lambda=0.019563
## + Fold05.Rep3: alpha=0.55008, lambda=0.600447
## - Fold05.Rep3: alpha=0.55008, lambda=0.600447
## + Fold05.Rep3: alpha=0.71987, lambda=0.017336
## - Fold05.Rep3: alpha=0.71987, lambda=0.017336
## + Fold05.Rep3: alpha=0.16961, lambda=0.086625
## - Fold05.Rep3: alpha=0.16961, lambda=0.086625
## + Fold05.Rep3: alpha=0.61948, lambda=0.011854
## - Fold05.Rep3: alpha=0.61948, lambda=0.011854
## + Fold05.Rep3: alpha=0.18579, lambda=0.002510
## - Fold05.Rep3: alpha=0.18579, lambda=0.002510
## + Fold05.Rep3: alpha=0.36092, lambda=0.018533
## - Fold05.Rep3: alpha=0.36092, lambda=0.018533
## + Fold06.Rep3: alpha=0.30285, lambda=0.004666
## - Fold06.Rep3: alpha=0.30285, lambda=0.004666
## + Fold06.Rep3: alpha=0.02355, lambda=0.061703
## - Fold06.Rep3: alpha=0.02355, lambda=0.061703
## + Fold06.Rep3: alpha=0.32050, lambda=0.005575
## - Fold06.Rep3: alpha=0.32050, lambda=0.005575
## + Fold06.Rep3: alpha=0.03179, lambda=0.019563
## - Fold06.Rep3: alpha=0.03179, lambda=0.019563
## + Fold06.Rep3: alpha=0.55008, lambda=0.600447
## - Fold06.Rep3: alpha=0.55008, lambda=0.600447
## + Fold06.Rep3: alpha=0.71987, lambda=0.017336
## - Fold06.Rep3: alpha=0.71987, lambda=0.017336
## + Fold06.Rep3: alpha=0.16961, lambda=0.086625
## - Fold06.Rep3: alpha=0.16961, lambda=0.086625
## + Fold06.Rep3: alpha=0.61948, lambda=0.011854
## - Fold06.Rep3: alpha=0.61948, lambda=0.011854
## + Fold06.Rep3: alpha=0.18579, lambda=0.002510
## - Fold06.Rep3: alpha=0.18579, lambda=0.002510
## + Fold06.Rep3: alpha=0.36092, lambda=0.018533
## - Fold06.Rep3: alpha=0.36092, lambda=0.018533
## + Fold07.Rep3: alpha=0.30285, lambda=0.004666
## - Fold07.Rep3: alpha=0.30285, lambda=0.004666
## + Fold07.Rep3: alpha=0.02355, lambda=0.061703
## - Fold07.Rep3: alpha=0.02355, lambda=0.061703
## + Fold07.Rep3: alpha=0.32050, lambda=0.005575
## - Fold07.Rep3: alpha=0.32050, lambda=0.005575
## + Fold07.Rep3: alpha=0.03179, lambda=0.019563
## - Fold07.Rep3: alpha=0.03179, lambda=0.019563
## + Fold07.Rep3: alpha=0.55008, lambda=0.600447
## - Fold07.Rep3: alpha=0.55008, lambda=0.600447
## + Fold07.Rep3: alpha=0.71987, lambda=0.017336
## - Fold07.Rep3: alpha=0.71987, lambda=0.017336
## + Fold07.Rep3: alpha=0.16961, lambda=0.086625
## - Fold07.Rep3: alpha=0.16961, lambda=0.086625
## + Fold07.Rep3: alpha=0.61948, lambda=0.011854
## - Fold07.Rep3: alpha=0.61948, lambda=0.011854
## + Fold07.Rep3: alpha=0.18579, lambda=0.002510
## - Fold07.Rep3: alpha=0.18579, lambda=0.002510
## + Fold07.Rep3: alpha=0.36092, lambda=0.018533
## - Fold07.Rep3: alpha=0.36092, lambda=0.018533
## + Fold08.Rep3: alpha=0.30285, lambda=0.004666
## - Fold08.Rep3: alpha=0.30285, lambda=0.004666
## + Fold08.Rep3: alpha=0.02355, lambda=0.061703
## - Fold08.Rep3: alpha=0.02355, lambda=0.061703
## + Fold08.Rep3: alpha=0.32050, lambda=0.005575
## - Fold08.Rep3: alpha=0.32050, lambda=0.005575
## + Fold08.Rep3: alpha=0.03179, lambda=0.019563
## - Fold08.Rep3: alpha=0.03179, lambda=0.019563
## + Fold08.Rep3: alpha=0.55008, lambda=0.600447
## - Fold08.Rep3: alpha=0.55008, lambda=0.600447
## + Fold08.Rep3: alpha=0.71987, lambda=0.017336
## - Fold08.Rep3: alpha=0.71987, lambda=0.017336
## + Fold08.Rep3: alpha=0.16961, lambda=0.086625
## - Fold08.Rep3: alpha=0.16961, lambda=0.086625
## + Fold08.Rep3: alpha=0.61948, lambda=0.011854
## - Fold08.Rep3: alpha=0.61948, lambda=0.011854
## + Fold08.Rep3: alpha=0.18579, lambda=0.002510
## - Fold08.Rep3: alpha=0.18579, lambda=0.002510
## + Fold08.Rep3: alpha=0.36092, lambda=0.018533
## - Fold08.Rep3: alpha=0.36092, lambda=0.018533
## + Fold09.Rep3: alpha=0.30285, lambda=0.004666
## - Fold09.Rep3: alpha=0.30285, lambda=0.004666
## + Fold09.Rep3: alpha=0.02355, lambda=0.061703
## - Fold09.Rep3: alpha=0.02355, lambda=0.061703
## + Fold09.Rep3: alpha=0.32050, lambda=0.005575
## - Fold09.Rep3: alpha=0.32050, lambda=0.005575
## + Fold09.Rep3: alpha=0.03179, lambda=0.019563
## - Fold09.Rep3: alpha=0.03179, lambda=0.019563
## + Fold09.Rep3: alpha=0.55008, lambda=0.600447
## - Fold09.Rep3: alpha=0.55008, lambda=0.600447
## + Fold09.Rep3: alpha=0.71987, lambda=0.017336
## - Fold09.Rep3: alpha=0.71987, lambda=0.017336
## + Fold09.Rep3: alpha=0.16961, lambda=0.086625
## - Fold09.Rep3: alpha=0.16961, lambda=0.086625
## + Fold09.Rep3: alpha=0.61948, lambda=0.011854
## - Fold09.Rep3: alpha=0.61948, lambda=0.011854
## + Fold09.Rep3: alpha=0.18579, lambda=0.002510
## - Fold09.Rep3: alpha=0.18579, lambda=0.002510
## + Fold09.Rep3: alpha=0.36092, lambda=0.018533
## - Fold09.Rep3: alpha=0.36092, lambda=0.018533
## + Fold10.Rep3: alpha=0.30285, lambda=0.004666
## - Fold10.Rep3: alpha=0.30285, lambda=0.004666
## + Fold10.Rep3: alpha=0.02355, lambda=0.061703
## - Fold10.Rep3: alpha=0.02355, lambda=0.061703
## + Fold10.Rep3: alpha=0.32050, lambda=0.005575
## - Fold10.Rep3: alpha=0.32050, lambda=0.005575
## + Fold10.Rep3: alpha=0.03179, lambda=0.019563
## - Fold10.Rep3: alpha=0.03179, lambda=0.019563
## + Fold10.Rep3: alpha=0.55008, lambda=0.600447
## - Fold10.Rep3: alpha=0.55008, lambda=0.600447
## + Fold10.Rep3: alpha=0.71987, lambda=0.017336
## - Fold10.Rep3: alpha=0.71987, lambda=0.017336
## + Fold10.Rep3: alpha=0.16961, lambda=0.086625
## - Fold10.Rep3: alpha=0.16961, lambda=0.086625
## + Fold10.Rep3: alpha=0.61948, lambda=0.011854
## - Fold10.Rep3: alpha=0.61948, lambda=0.011854
## + Fold10.Rep3: alpha=0.18579, lambda=0.002510
## - Fold10.Rep3: alpha=0.18579, lambda=0.002510
## + Fold10.Rep3: alpha=0.36092, lambda=0.018533
## - Fold10.Rep3: alpha=0.36092, lambda=0.018533
## + Fold01.Rep4: alpha=0.30285, lambda=0.004666
## - Fold01.Rep4: alpha=0.30285, lambda=0.004666
## + Fold01.Rep4: alpha=0.02355, lambda=0.061703
## - Fold01.Rep4: alpha=0.02355, lambda=0.061703
## + Fold01.Rep4: alpha=0.32050, lambda=0.005575
## - Fold01.Rep4: alpha=0.32050, lambda=0.005575
## + Fold01.Rep4: alpha=0.03179, lambda=0.019563
## - Fold01.Rep4: alpha=0.03179, lambda=0.019563
## + Fold01.Rep4: alpha=0.55008, lambda=0.600447
## - Fold01.Rep4: alpha=0.55008, lambda=0.600447
## + Fold01.Rep4: alpha=0.71987, lambda=0.017336
## - Fold01.Rep4: alpha=0.71987, lambda=0.017336
## + Fold01.Rep4: alpha=0.16961, lambda=0.086625
## - Fold01.Rep4: alpha=0.16961, lambda=0.086625
## + Fold01.Rep4: alpha=0.61948, lambda=0.011854
## - Fold01.Rep4: alpha=0.61948, lambda=0.011854
## + Fold01.Rep4: alpha=0.18579, lambda=0.002510
## - Fold01.Rep4: alpha=0.18579, lambda=0.002510
## + Fold01.Rep4: alpha=0.36092, lambda=0.018533
## - Fold01.Rep4: alpha=0.36092, lambda=0.018533
## + Fold02.Rep4: alpha=0.30285, lambda=0.004666
## - Fold02.Rep4: alpha=0.30285, lambda=0.004666
## + Fold02.Rep4: alpha=0.02355, lambda=0.061703
## - Fold02.Rep4: alpha=0.02355, lambda=0.061703
## + Fold02.Rep4: alpha=0.32050, lambda=0.005575
## - Fold02.Rep4: alpha=0.32050, lambda=0.005575
## + Fold02.Rep4: alpha=0.03179, lambda=0.019563
## - Fold02.Rep4: alpha=0.03179, lambda=0.019563
## + Fold02.Rep4: alpha=0.55008, lambda=0.600447
## - Fold02.Rep4: alpha=0.55008, lambda=0.600447
## + Fold02.Rep4: alpha=0.71987, lambda=0.017336
## - Fold02.Rep4: alpha=0.71987, lambda=0.017336
## + Fold02.Rep4: alpha=0.16961, lambda=0.086625
## - Fold02.Rep4: alpha=0.16961, lambda=0.086625
## + Fold02.Rep4: alpha=0.61948, lambda=0.011854
## - Fold02.Rep4: alpha=0.61948, lambda=0.011854
## + Fold02.Rep4: alpha=0.18579, lambda=0.002510
## - Fold02.Rep4: alpha=0.18579, lambda=0.002510
## + Fold02.Rep4: alpha=0.36092, lambda=0.018533
## - Fold02.Rep4: alpha=0.36092, lambda=0.018533
## + Fold03.Rep4: alpha=0.30285, lambda=0.004666
## - Fold03.Rep4: alpha=0.30285, lambda=0.004666
## + Fold03.Rep4: alpha=0.02355, lambda=0.061703
## - Fold03.Rep4: alpha=0.02355, lambda=0.061703
## + Fold03.Rep4: alpha=0.32050, lambda=0.005575
## - Fold03.Rep4: alpha=0.32050, lambda=0.005575
## + Fold03.Rep4: alpha=0.03179, lambda=0.019563
## - Fold03.Rep4: alpha=0.03179, lambda=0.019563
## + Fold03.Rep4: alpha=0.55008, lambda=0.600447
## - Fold03.Rep4: alpha=0.55008, lambda=0.600447
## + Fold03.Rep4: alpha=0.71987, lambda=0.017336
## - Fold03.Rep4: alpha=0.71987, lambda=0.017336
## + Fold03.Rep4: alpha=0.16961, lambda=0.086625
## - Fold03.Rep4: alpha=0.16961, lambda=0.086625
## + Fold03.Rep4: alpha=0.61948, lambda=0.011854
## - Fold03.Rep4: alpha=0.61948, lambda=0.011854
## + Fold03.Rep4: alpha=0.18579, lambda=0.002510
## - Fold03.Rep4: alpha=0.18579, lambda=0.002510
## + Fold03.Rep4: alpha=0.36092, lambda=0.018533
## - Fold03.Rep4: alpha=0.36092, lambda=0.018533
## + Fold04.Rep4: alpha=0.30285, lambda=0.004666
## - Fold04.Rep4: alpha=0.30285, lambda=0.004666
## + Fold04.Rep4: alpha=0.02355, lambda=0.061703
## - Fold04.Rep4: alpha=0.02355, lambda=0.061703
## + Fold04.Rep4: alpha=0.32050, lambda=0.005575
## - Fold04.Rep4: alpha=0.32050, lambda=0.005575
## + Fold04.Rep4: alpha=0.03179, lambda=0.019563
## - Fold04.Rep4: alpha=0.03179, lambda=0.019563
## + Fold04.Rep4: alpha=0.55008, lambda=0.600447
## - Fold04.Rep4: alpha=0.55008, lambda=0.600447
## + Fold04.Rep4: alpha=0.71987, lambda=0.017336
## - Fold04.Rep4: alpha=0.71987, lambda=0.017336
## + Fold04.Rep4: alpha=0.16961, lambda=0.086625
## - Fold04.Rep4: alpha=0.16961, lambda=0.086625
## + Fold04.Rep4: alpha=0.61948, lambda=0.011854
## - Fold04.Rep4: alpha=0.61948, lambda=0.011854
## + Fold04.Rep4: alpha=0.18579, lambda=0.002510
## - Fold04.Rep4: alpha=0.18579, lambda=0.002510
## + Fold04.Rep4: alpha=0.36092, lambda=0.018533
## - Fold04.Rep4: alpha=0.36092, lambda=0.018533
## + Fold05.Rep4: alpha=0.30285, lambda=0.004666
## - Fold05.Rep4: alpha=0.30285, lambda=0.004666
## + Fold05.Rep4: alpha=0.02355, lambda=0.061703
## - Fold05.Rep4: alpha=0.02355, lambda=0.061703
## + Fold05.Rep4: alpha=0.32050, lambda=0.005575
## - Fold05.Rep4: alpha=0.32050, lambda=0.005575
## + Fold05.Rep4: alpha=0.03179, lambda=0.019563
## - Fold05.Rep4: alpha=0.03179, lambda=0.019563
## + Fold05.Rep4: alpha=0.55008, lambda=0.600447
## - Fold05.Rep4: alpha=0.55008, lambda=0.600447
## + Fold05.Rep4: alpha=0.71987, lambda=0.017336
## - Fold05.Rep4: alpha=0.71987, lambda=0.017336
## + Fold05.Rep4: alpha=0.16961, lambda=0.086625
## - Fold05.Rep4: alpha=0.16961, lambda=0.086625
## + Fold05.Rep4: alpha=0.61948, lambda=0.011854
## - Fold05.Rep4: alpha=0.61948, lambda=0.011854
## + Fold05.Rep4: alpha=0.18579, lambda=0.002510
## - Fold05.Rep4: alpha=0.18579, lambda=0.002510
## + Fold05.Rep4: alpha=0.36092, lambda=0.018533
## - Fold05.Rep4: alpha=0.36092, lambda=0.018533
## + Fold06.Rep4: alpha=0.30285, lambda=0.004666
## - Fold06.Rep4: alpha=0.30285, lambda=0.004666
## + Fold06.Rep4: alpha=0.02355, lambda=0.061703
## - Fold06.Rep4: alpha=0.02355, lambda=0.061703
## + Fold06.Rep4: alpha=0.32050, lambda=0.005575
## - Fold06.Rep4: alpha=0.32050, lambda=0.005575
## + Fold06.Rep4: alpha=0.03179, lambda=0.019563
## - Fold06.Rep4: alpha=0.03179, lambda=0.019563
## + Fold06.Rep4: alpha=0.55008, lambda=0.600447
## - Fold06.Rep4: alpha=0.55008, lambda=0.600447
## + Fold06.Rep4: alpha=0.71987, lambda=0.017336
## - Fold06.Rep4: alpha=0.71987, lambda=0.017336
## + Fold06.Rep4: alpha=0.16961, lambda=0.086625
## - Fold06.Rep4: alpha=0.16961, lambda=0.086625
## + Fold06.Rep4: alpha=0.61948, lambda=0.011854
## - Fold06.Rep4: alpha=0.61948, lambda=0.011854
## + Fold06.Rep4: alpha=0.18579, lambda=0.002510
## - Fold06.Rep4: alpha=0.18579, lambda=0.002510
## + Fold06.Rep4: alpha=0.36092, lambda=0.018533
## - Fold06.Rep4: alpha=0.36092, lambda=0.018533
## + Fold07.Rep4: alpha=0.30285, lambda=0.004666
## - Fold07.Rep4: alpha=0.30285, lambda=0.004666
## + Fold07.Rep4: alpha=0.02355, lambda=0.061703
## - Fold07.Rep4: alpha=0.02355, lambda=0.061703
## + Fold07.Rep4: alpha=0.32050, lambda=0.005575
## - Fold07.Rep4: alpha=0.32050, lambda=0.005575
## + Fold07.Rep4: alpha=0.03179, lambda=0.019563
## - Fold07.Rep4: alpha=0.03179, lambda=0.019563
## + Fold07.Rep4: alpha=0.55008, lambda=0.600447
## - Fold07.Rep4: alpha=0.55008, lambda=0.600447
## + Fold07.Rep4: alpha=0.71987, lambda=0.017336
## - Fold07.Rep4: alpha=0.71987, lambda=0.017336
## + Fold07.Rep4: alpha=0.16961, lambda=0.086625
## - Fold07.Rep4: alpha=0.16961, lambda=0.086625
## + Fold07.Rep4: alpha=0.61948, lambda=0.011854
## - Fold07.Rep4: alpha=0.61948, lambda=0.011854
## + Fold07.Rep4: alpha=0.18579, lambda=0.002510
## - Fold07.Rep4: alpha=0.18579, lambda=0.002510
## + Fold07.Rep4: alpha=0.36092, lambda=0.018533
## - Fold07.Rep4: alpha=0.36092, lambda=0.018533
## + Fold08.Rep4: alpha=0.30285, lambda=0.004666
## - Fold08.Rep4: alpha=0.30285, lambda=0.004666
## + Fold08.Rep4: alpha=0.02355, lambda=0.061703
## - Fold08.Rep4: alpha=0.02355, lambda=0.061703
## + Fold08.Rep4: alpha=0.32050, lambda=0.005575
## - Fold08.Rep4: alpha=0.32050, lambda=0.005575
## + Fold08.Rep4: alpha=0.03179, lambda=0.019563
## - Fold08.Rep4: alpha=0.03179, lambda=0.019563
## + Fold08.Rep4: alpha=0.55008, lambda=0.600447
## - Fold08.Rep4: alpha=0.55008, lambda=0.600447
## + Fold08.Rep4: alpha=0.71987, lambda=0.017336
## - Fold08.Rep4: alpha=0.71987, lambda=0.017336
## + Fold08.Rep4: alpha=0.16961, lambda=0.086625
## - Fold08.Rep4: alpha=0.16961, lambda=0.086625
## + Fold08.Rep4: alpha=0.61948, lambda=0.011854
## - Fold08.Rep4: alpha=0.61948, lambda=0.011854
## + Fold08.Rep4: alpha=0.18579, lambda=0.002510
## - Fold08.Rep4: alpha=0.18579, lambda=0.002510
## + Fold08.Rep4: alpha=0.36092, lambda=0.018533
## - Fold08.Rep4: alpha=0.36092, lambda=0.018533
## + Fold09.Rep4: alpha=0.30285, lambda=0.004666
## - Fold09.Rep4: alpha=0.30285, lambda=0.004666
## + Fold09.Rep4: alpha=0.02355, lambda=0.061703
## - Fold09.Rep4: alpha=0.02355, lambda=0.061703
## + Fold09.Rep4: alpha=0.32050, lambda=0.005575
## - Fold09.Rep4: alpha=0.32050, lambda=0.005575
## + Fold09.Rep4: alpha=0.03179, lambda=0.019563
## - Fold09.Rep4: alpha=0.03179, lambda=0.019563
## + Fold09.Rep4: alpha=0.55008, lambda=0.600447
## - Fold09.Rep4: alpha=0.55008, lambda=0.600447
## + Fold09.Rep4: alpha=0.71987, lambda=0.017336
## - Fold09.Rep4: alpha=0.71987, lambda=0.017336
## + Fold09.Rep4: alpha=0.16961, lambda=0.086625
## - Fold09.Rep4: alpha=0.16961, lambda=0.086625
## + Fold09.Rep4: alpha=0.61948, lambda=0.011854
## - Fold09.Rep4: alpha=0.61948, lambda=0.011854
## + Fold09.Rep4: alpha=0.18579, lambda=0.002510
## - Fold09.Rep4: alpha=0.18579, lambda=0.002510
## + Fold09.Rep4: alpha=0.36092, lambda=0.018533
## - Fold09.Rep4: alpha=0.36092, lambda=0.018533
## + Fold10.Rep4: alpha=0.30285, lambda=0.004666
## - Fold10.Rep4: alpha=0.30285, lambda=0.004666
## + Fold10.Rep4: alpha=0.02355, lambda=0.061703
## - Fold10.Rep4: alpha=0.02355, lambda=0.061703
## + Fold10.Rep4: alpha=0.32050, lambda=0.005575
## - Fold10.Rep4: alpha=0.32050, lambda=0.005575
## + Fold10.Rep4: alpha=0.03179, lambda=0.019563
## - Fold10.Rep4: alpha=0.03179, lambda=0.019563
## + Fold10.Rep4: alpha=0.55008, lambda=0.600447
## - Fold10.Rep4: alpha=0.55008, lambda=0.600447
## + Fold10.Rep4: alpha=0.71987, lambda=0.017336
## - Fold10.Rep4: alpha=0.71987, lambda=0.017336
## + Fold10.Rep4: alpha=0.16961, lambda=0.086625
## - Fold10.Rep4: alpha=0.16961, lambda=0.086625
## + Fold10.Rep4: alpha=0.61948, lambda=0.011854
## - Fold10.Rep4: alpha=0.61948, lambda=0.011854
## + Fold10.Rep4: alpha=0.18579, lambda=0.002510
## - Fold10.Rep4: alpha=0.18579, lambda=0.002510
## + Fold10.Rep4: alpha=0.36092, lambda=0.018533
## - Fold10.Rep4: alpha=0.36092, lambda=0.018533
## + Fold01.Rep5: alpha=0.30285, lambda=0.004666
## - Fold01.Rep5: alpha=0.30285, lambda=0.004666
## + Fold01.Rep5: alpha=0.02355, lambda=0.061703
## - Fold01.Rep5: alpha=0.02355, lambda=0.061703
## + Fold01.Rep5: alpha=0.32050, lambda=0.005575
## - Fold01.Rep5: alpha=0.32050, lambda=0.005575
## + Fold01.Rep5: alpha=0.03179, lambda=0.019563
## - Fold01.Rep5: alpha=0.03179, lambda=0.019563
## + Fold01.Rep5: alpha=0.55008, lambda=0.600447
## - Fold01.Rep5: alpha=0.55008, lambda=0.600447
## + Fold01.Rep5: alpha=0.71987, lambda=0.017336
## - Fold01.Rep5: alpha=0.71987, lambda=0.017336
## + Fold01.Rep5: alpha=0.16961, lambda=0.086625
## - Fold01.Rep5: alpha=0.16961, lambda=0.086625
## + Fold01.Rep5: alpha=0.61948, lambda=0.011854
## - Fold01.Rep5: alpha=0.61948, lambda=0.011854
## + Fold01.Rep5: alpha=0.18579, lambda=0.002510
## - Fold01.Rep5: alpha=0.18579, lambda=0.002510
## + Fold01.Rep5: alpha=0.36092, lambda=0.018533
## - Fold01.Rep5: alpha=0.36092, lambda=0.018533
## + Fold02.Rep5: alpha=0.30285, lambda=0.004666
## - Fold02.Rep5: alpha=0.30285, lambda=0.004666
## + Fold02.Rep5: alpha=0.02355, lambda=0.061703
## - Fold02.Rep5: alpha=0.02355, lambda=0.061703
## + Fold02.Rep5: alpha=0.32050, lambda=0.005575
## - Fold02.Rep5: alpha=0.32050, lambda=0.005575
## + Fold02.Rep5: alpha=0.03179, lambda=0.019563
## - Fold02.Rep5: alpha=0.03179, lambda=0.019563
## + Fold02.Rep5: alpha=0.55008, lambda=0.600447
## - Fold02.Rep5: alpha=0.55008, lambda=0.600447
## + Fold02.Rep5: alpha=0.71987, lambda=0.017336
## - Fold02.Rep5: alpha=0.71987, lambda=0.017336
## + Fold02.Rep5: alpha=0.16961, lambda=0.086625
## - Fold02.Rep5: alpha=0.16961, lambda=0.086625
## + Fold02.Rep5: alpha=0.61948, lambda=0.011854
## - Fold02.Rep5: alpha=0.61948, lambda=0.011854
## + Fold02.Rep5: alpha=0.18579, lambda=0.002510
## - Fold02.Rep5: alpha=0.18579, lambda=0.002510
## + Fold02.Rep5: alpha=0.36092, lambda=0.018533
## - Fold02.Rep5: alpha=0.36092, lambda=0.018533
## + Fold03.Rep5: alpha=0.30285, lambda=0.004666
## - Fold03.Rep5: alpha=0.30285, lambda=0.004666
## + Fold03.Rep5: alpha=0.02355, lambda=0.061703
## - Fold03.Rep5: alpha=0.02355, lambda=0.061703
## + Fold03.Rep5: alpha=0.32050, lambda=0.005575
## - Fold03.Rep5: alpha=0.32050, lambda=0.005575
## + Fold03.Rep5: alpha=0.03179, lambda=0.019563
## - Fold03.Rep5: alpha=0.03179, lambda=0.019563
## + Fold03.Rep5: alpha=0.55008, lambda=0.600447
## - Fold03.Rep5: alpha=0.55008, lambda=0.600447
## + Fold03.Rep5: alpha=0.71987, lambda=0.017336
## - Fold03.Rep5: alpha=0.71987, lambda=0.017336
## + Fold03.Rep5: alpha=0.16961, lambda=0.086625
## - Fold03.Rep5: alpha=0.16961, lambda=0.086625
## + Fold03.Rep5: alpha=0.61948, lambda=0.011854
## - Fold03.Rep5: alpha=0.61948, lambda=0.011854
## + Fold03.Rep5: alpha=0.18579, lambda=0.002510
## - Fold03.Rep5: alpha=0.18579, lambda=0.002510
## + Fold03.Rep5: alpha=0.36092, lambda=0.018533
## - Fold03.Rep5: alpha=0.36092, lambda=0.018533
## + Fold04.Rep5: alpha=0.30285, lambda=0.004666
## - Fold04.Rep5: alpha=0.30285, lambda=0.004666
## + Fold04.Rep5: alpha=0.02355, lambda=0.061703
## - Fold04.Rep5: alpha=0.02355, lambda=0.061703
## + Fold04.Rep5: alpha=0.32050, lambda=0.005575
## - Fold04.Rep5: alpha=0.32050, lambda=0.005575
## + Fold04.Rep5: alpha=0.03179, lambda=0.019563
## - Fold04.Rep5: alpha=0.03179, lambda=0.019563
## + Fold04.Rep5: alpha=0.55008, lambda=0.600447
## - Fold04.Rep5: alpha=0.55008, lambda=0.600447
## + Fold04.Rep5: alpha=0.71987, lambda=0.017336
## - Fold04.Rep5: alpha=0.71987, lambda=0.017336
## + Fold04.Rep5: alpha=0.16961, lambda=0.086625
## - Fold04.Rep5: alpha=0.16961, lambda=0.086625
## + Fold04.Rep5: alpha=0.61948, lambda=0.011854
## - Fold04.Rep5: alpha=0.61948, lambda=0.011854
## + Fold04.Rep5: alpha=0.18579, lambda=0.002510
## - Fold04.Rep5: alpha=0.18579, lambda=0.002510
## + Fold04.Rep5: alpha=0.36092, lambda=0.018533
## - Fold04.Rep5: alpha=0.36092, lambda=0.018533
## + Fold05.Rep5: alpha=0.30285, lambda=0.004666
## - Fold05.Rep5: alpha=0.30285, lambda=0.004666
## + Fold05.Rep5: alpha=0.02355, lambda=0.061703
## - Fold05.Rep5: alpha=0.02355, lambda=0.061703
## + Fold05.Rep5: alpha=0.32050, lambda=0.005575
## - Fold05.Rep5: alpha=0.32050, lambda=0.005575
## + Fold05.Rep5: alpha=0.03179, lambda=0.019563
## - Fold05.Rep5: alpha=0.03179, lambda=0.019563
## + Fold05.Rep5: alpha=0.55008, lambda=0.600447
## - Fold05.Rep5: alpha=0.55008, lambda=0.600447
## + Fold05.Rep5: alpha=0.71987, lambda=0.017336
## - Fold05.Rep5: alpha=0.71987, lambda=0.017336
## + Fold05.Rep5: alpha=0.16961, lambda=0.086625
## - Fold05.Rep5: alpha=0.16961, lambda=0.086625
## + Fold05.Rep5: alpha=0.61948, lambda=0.011854
## - Fold05.Rep5: alpha=0.61948, lambda=0.011854
## + Fold05.Rep5: alpha=0.18579, lambda=0.002510
## - Fold05.Rep5: alpha=0.18579, lambda=0.002510
## + Fold05.Rep5: alpha=0.36092, lambda=0.018533
## - Fold05.Rep5: alpha=0.36092, lambda=0.018533
## + Fold06.Rep5: alpha=0.30285, lambda=0.004666
## - Fold06.Rep5: alpha=0.30285, lambda=0.004666
## + Fold06.Rep5: alpha=0.02355, lambda=0.061703
## - Fold06.Rep5: alpha=0.02355, lambda=0.061703
## + Fold06.Rep5: alpha=0.32050, lambda=0.005575
## - Fold06.Rep5: alpha=0.32050, lambda=0.005575
## + Fold06.Rep5: alpha=0.03179, lambda=0.019563
## - Fold06.Rep5: alpha=0.03179, lambda=0.019563
## + Fold06.Rep5: alpha=0.55008, lambda=0.600447
## - Fold06.Rep5: alpha=0.55008, lambda=0.600447
## + Fold06.Rep5: alpha=0.71987, lambda=0.017336
## - Fold06.Rep5: alpha=0.71987, lambda=0.017336
## + Fold06.Rep5: alpha=0.16961, lambda=0.086625
## - Fold06.Rep5: alpha=0.16961, lambda=0.086625
## + Fold06.Rep5: alpha=0.61948, lambda=0.011854
## - Fold06.Rep5: alpha=0.61948, lambda=0.011854
## + Fold06.Rep5: alpha=0.18579, lambda=0.002510
## - Fold06.Rep5: alpha=0.18579, lambda=0.002510
## + Fold06.Rep5: alpha=0.36092, lambda=0.018533
## - Fold06.Rep5: alpha=0.36092, lambda=0.018533
## + Fold07.Rep5: alpha=0.30285, lambda=0.004666
## - Fold07.Rep5: alpha=0.30285, lambda=0.004666
## + Fold07.Rep5: alpha=0.02355, lambda=0.061703
## - Fold07.Rep5: alpha=0.02355, lambda=0.061703
## + Fold07.Rep5: alpha=0.32050, lambda=0.005575
## - Fold07.Rep5: alpha=0.32050, lambda=0.005575
## + Fold07.Rep5: alpha=0.03179, lambda=0.019563
## - Fold07.Rep5: alpha=0.03179, lambda=0.019563
## + Fold07.Rep5: alpha=0.55008, lambda=0.600447
## - Fold07.Rep5: alpha=0.55008, lambda=0.600447
## + Fold07.Rep5: alpha=0.71987, lambda=0.017336
## - Fold07.Rep5: alpha=0.71987, lambda=0.017336
## + Fold07.Rep5: alpha=0.16961, lambda=0.086625
## - Fold07.Rep5: alpha=0.16961, lambda=0.086625
## + Fold07.Rep5: alpha=0.61948, lambda=0.011854
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## + Fold07.Rep5: alpha=0.18579, lambda=0.002510
## - Fold07.Rep5: alpha=0.18579, lambda=0.002510
## + Fold07.Rep5: alpha=0.36092, lambda=0.018533
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## + Fold08.Rep5: alpha=0.30285, lambda=0.004666
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## + Fold08.Rep5: alpha=0.02355, lambda=0.061703
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## + Fold08.Rep5: alpha=0.32050, lambda=0.005575
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## + Fold08.Rep5: alpha=0.03179, lambda=0.019563
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## + Fold08.Rep5: alpha=0.61948, lambda=0.011854
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## + Fold08.Rep5: alpha=0.18579, lambda=0.002510
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## + Fold08.Rep5: alpha=0.36092, lambda=0.018533
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## + Fold09.Rep5: alpha=0.32050, lambda=0.005575
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## + Fold09.Rep5: alpha=0.03179, lambda=0.019563
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## + Fold09.Rep5: alpha=0.55008, lambda=0.600447
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## + Fold09.Rep5: alpha=0.71987, lambda=0.017336
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## + Fold09.Rep5: alpha=0.16961, lambda=0.086625
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## + Fold09.Rep5: alpha=0.61948, lambda=0.011854
## - Fold09.Rep5: alpha=0.61948, lambda=0.011854
## + Fold09.Rep5: alpha=0.18579, lambda=0.002510
## - Fold09.Rep5: alpha=0.18579, lambda=0.002510
## + Fold09.Rep5: alpha=0.36092, lambda=0.018533
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## + Fold10.Rep5: alpha=0.30285, lambda=0.004666
## - Fold10.Rep5: alpha=0.30285, lambda=0.004666
## + Fold10.Rep5: alpha=0.02355, lambda=0.061703
## - Fold10.Rep5: alpha=0.02355, lambda=0.061703
## + Fold10.Rep5: alpha=0.32050, lambda=0.005575
## - Fold10.Rep5: alpha=0.32050, lambda=0.005575
## + Fold10.Rep5: alpha=0.03179, lambda=0.019563
## - Fold10.Rep5: alpha=0.03179, lambda=0.019563
## + Fold10.Rep5: alpha=0.55008, lambda=0.600447
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## + Fold10.Rep5: alpha=0.71987, lambda=0.017336
## - Fold10.Rep5: alpha=0.71987, lambda=0.017336
## + Fold10.Rep5: alpha=0.16961, lambda=0.086625
## - Fold10.Rep5: alpha=0.16961, lambda=0.086625
## + Fold10.Rep5: alpha=0.61948, lambda=0.011854
## - Fold10.Rep5: alpha=0.61948, lambda=0.011854
## + Fold10.Rep5: alpha=0.18579, lambda=0.002510
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## + Fold10.Rep5: alpha=0.36092, lambda=0.018533
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## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 0.361, lambda = 0.0185 on full training set
# Best tuning parameter
elastic_reg$bestTune
## alpha lambda
## 7 0.3609182 0.01853285
# Make predictions on training set
predictions_train <- predict(elastic_reg, x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6365787 0.3650057
# Make predictions on test set
predictions_test <- predict(elastic_reg, x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6693786 0.3435866
colnames(df)
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
ggplot(data = df, mapping = aes(x = total.sulfur.dioxide, y = quality)) +
geom_point()
ggplot(data = df, mapping = aes(x = residual.sugar, y = quality)) +
geom_point()
There is really no relationship. This is probably an exercise in clusterting or machine learning, but linear regression is insufficient.
ggplot(data = df, mapping = aes(x = alcohol, y = quality)) +
geom_point() +
geom_smooth()
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'